On the formation of planets and moons

We may expect that some other stars in our galaxy have planetary systems like our own. If they do, do all their planets orbit their Sun in the same direction, as in our solar system? A similar question can be asked of the moons about the planets. Does the fact that they are a common occurance in our solar system and that they almost all rotate in the same direction around the planet mean that this is normal for all planetary systems? The obvious starting point is to consider how the Earth's moon was formed. Was the moon formed for example, from a close encounter of the Earth with a large comet as one common theory suggests, and if so were the other moons in the solar system formed the same way?

The the common occurance of moons about the planets of the solar system as well as their similarities in the direction of rotation, suggests that there are physical processes at work which naturally produce this arrangement. To try and find a plausible reason for this, consider first the structure of our galaxy. It is a typical galaxy with well developed spiral arms. The occurance of these spiral arms indicates that the centre is rotating faster than the outer regions. Thus we may anticipate that for the matter which formed the solar system, its velocity varied depending on its distance from the centre of the galaxy. This slight shear in the matter forming the solar system represents an angular rotation which would be captured when the matter came together to form the solar system as we know it.

As the matter collapsed to form the Sun, any slight rotation in the matter is concentrated, rather like the bath water spinning when it goes down the plughole. For an isolated system in space, this rotation or angular momentum remains constant with time for that system. That is, the matter may form one body or split into several bodies at various times but the total angular momentum remains constant. However the angular momentum may not remain constant if a large body from outside the system makes a close approach, because angular momentum may be transferred from the system to the body or vise-versa.

The Sun is held together as a single body by gravity, whereas its rotation tries to tear it apart. The balance between the amount of mass and the rotation speed determines whether the collapsing matter settles down to form a single body, a body with planets, or throws matter off which is able to escape the Sun's gravitational influence altogether. So what is the balance in the solar system? Is there enough angular momentum to require that planets will form? Before we attempt to answer that question we first ask the same question of the much simpler Earth-Moon system. That is, does the Earth-Moon system have enough angular momentum to require the Moon to form? If so is the amount of angular momentum similar or smaller than the amount in the solar system as a whole, such that we might expect that the Earth-Moon system to have been formed from collapsing matter with this amount of angular momentum.

The angular momentum of the Earth-Moon system is the sum of that in the orbit of the Moon about the Earth and that of the rotation of the Earth on its axis. Any other contributions from comets etc. is not sufficient to be significant. The angular momentum of a body in circular orbit is proportional to its mass, its radius from the central body (the Earth in this case) and its orbital velocity. The angular momentum of a spinning body is its moment of inertia times its angular velocity. In the case of a sphere this is a quarter the mass of the body times the radius of the surface times the velocity at the equator. Using known values for these quantities, the angular momentum of the Moon is found to be about 5 times that of the spinning Earth. That is if the Moon were to become part of the Earth, the Earth would have to rotate 6 times as fast to maintain the same angular momentum. Under such rotation we might suspect the Earth would be unstable and break up. This is difficult to calculate theoretically, but it can be tested with a computer simulation. Simulations set to reflect the mass and angular momentum of the Earth-Moon system show that there is more than enough rotation to cause breakup of the central body and the likely formation of a moon. However this does not exclude the Moon from being created by a passing comet, because the existing rotation might have been introduced by such an event.

To assess whether the angular momentum of the Earth-Moon system could occur naturally, we compare it with the level of angular momentum within the solar system. If the angular momentum of the Earth-Moon system is comparable or less than that of the solar system in general, then it is possible for the Moon to form naturally without invoking passing comets or other external influences. The mean angular momentum of the solar system can be calculated by adding the angular momentum of the planets and the Sun's rotation and deviding by the total mass of all the bodies. This computation shows that the mean angular momentum of the solar system is considerably greater than that of the Earth-Moon system. Thus not only is there in general sufficient angular momentum to fling off the Moon, but it is possible that other "moons" were shed which escaped Earth gravity and finished up as part of another planet.

The level of angular momentum in the solar system makes planets a natural consequence of the Sun's formation. If this level of angular momentum is typical throughout the galaxy, we would expect most stars to have planets around them (or be double stars), and for many of these planets to have moons. Whether the angular momentum of the solar system is typical we might assess from the average level of angular momentum in the galaxy. Such a value is more difficult. Should anyone derive such a value I would be pleased to hear about it.

Copies of a moon formation simulation program and the solar system anular momentum calculation may be obtained from the author

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Last modified April 04.